Download or read book A Review of Numerous Parallel Multigrid Methods written by International Business Machines Corporation. Research Division and published by . This book was released on 1995 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "Parallel multilevel methods are shown to be the natural precursors to standard multilevel methods based on the personnel computing era of earlier this century. They are also the natural successors to standard multilevel methods in the age of computers. What makes six parallel multilevel methods practical and impractical is discussed in the context of the three algorithms that encapsulate them."
Download or read book Numerical Solution of Partial Differential Equations on Parallel Computers written by Are Magnus Bruaset and published by Springer Science & Business Media. This book was released on 2006-03-05 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the dawn of computing, the quest for a better understanding of Nature has been a driving force for technological development. Groundbreaking achievements by great scientists have paved the way from the abacus to the supercomputing power of today. When trying to replicate Nature in the computer’s silicon test tube, there is need for precise and computable process descriptions. The scienti?c ?elds of Ma- ematics and Physics provide a powerful vehicle for such descriptions in terms of Partial Differential Equations (PDEs). Formulated as such equations, physical laws can become subject to computational and analytical studies. In the computational setting, the equations can be discreti ed for ef?cient solution on a computer, leading to valuable tools for simulation of natural and man-made processes. Numerical so- tion of PDE-based mathematical models has been an important research topic over centuries, and will remain so for centuries to come. In the context of computer-based simulations, the quality of the computed results is directly connected to the model’s complexity and the number of data points used for the computations. Therefore, computational scientists tend to ?ll even the largest and most powerful computers they can get access to, either by increasing the si e of the data sets, or by introducing new model terms that make the simulations more realistic, or a combination of both. Today, many important simulation problems can not be solved by one single computer, but calls for parallel computing.
Download or read book Analysis of a Parallel Multigrid Algorithm written by National Aeronautics and Space Adm Nasa and published by Independently Published. This book was released on 2018-10-24 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: The parallel multigrid algorithm of Frederickson and McBryan (1987) is considered. This algorithm uses multiple coarse-grid problems (instead of one problem) in the hope of accelerating convergence and is found to have a close relationship to traditional multigrid methods. Specifically, the parallel coarse-grid correction operator is identical to a traditional multigrid coarse-grid correction operator, except that the mixing of high and low frequencies caused by aliasing error is removed. Appropriate relaxation operators can be chosen to take advantage of this property. Comparisons between the standard multigrid and the new method are made. Chan, Tony F. and Tuminaro, Ray S. Unspecified Center DE-FG03-87ER-25037; DAAL03-88-K-0085; NSF DMS-87-14612; NCC2-387; NCA2-233...
Download or read book Matrix Based Multigrid written by Yair Shapira and published by Springer Science & Business Media. This book was released on 2008-07-02 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: Matrix-Based Multigrid introduces and analyzes the multigrid approach for the numerical solution of large sparse linear systems arising from the discretization of elliptic partial differential equations. Special attention is given to the powerful matrix-based-multigrid approach, which is particularly useful for problems with variable coefficients and nonsymmetric and indefinite problems. This book can be used as a textbook in courses in numerical analysis, numerical linear algebra, and numerical PDEs at the advanced undergraduate and graduate levels in computer science, math, and applied math departments. The theory is written in simple algebraic terms and therefore requires preliminary knowledge only in basic linear algebra and calculus.
Download or read book Applications on Advanced Architecture Computers written by Greg Astfalk and published by SIAM. This book was released on 1996-01-01 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume conveniently brings together updated versions of 30 articles that originally appeared in SIAM News from 1990 to 1995. The objective of the column from which the articles are taken is to present applications that have been successfully treated on advanced architecture computers. Astfalk edits this popular series of articles in SIAM's flagship publication, SIAM News. Algorithmic issues addressed are those which have found general use in building parallel codes for solving problems. In addition to updates that reflect advances and changes in the field of applications on advanced architecture computers, Astfalk has added an index and introductory comments to each article, making this book cohesive and interesting to practitioners and researchers alike.
Download or read book A Journey through the History of Numerical Linear Algebra written by Claude Brezinski and published by SIAM. This book was released on 2022-12-06 with total page 813 pages. Available in PDF, EPUB and Kindle. Book excerpt: This expansive volume describes the history of numerical methods proposed for solving linear algebra problems, from antiquity to the present day. The authors focus on methods for linear systems of equations and eigenvalue problems and describe the interplay between numerical methods and the computing tools available at the time. The second part of the book consists of 78 biographies of important contributors to the field. A Journey through the History of Numerical Linear Algebra will be of special interest to applied mathematicians, especially researchers in numerical linear algebra, people involved in scientific computing, and historians of mathematics.
Download or read book Russian Journal of Numerical Analysis and Mathematical Modelling written by and published by . This book was released on 2003 with total page 580 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Computer Solution of Large Linear Systems written by Gerard Meurant and published by Elsevier. This book was released on 1999-06-16 with total page 777 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with numerical methods for solving large sparse linear systems of equations, particularly those arising from the discretization of partial differential equations. It covers both direct and iterative methods. Direct methods which are considered are variants of Gaussian elimination and fast solvers for separable partial differential equations in rectangular domains. The book reviews the classical iterative methods like Jacobi, Gauss-Seidel and alternating directions algorithms. A particular emphasis is put on the conjugate gradient as well as conjugate gradient -like methods for non symmetric problems. Most efficient preconditioners used to speed up convergence are studied. A chapter is devoted to the multigrid method and the book ends with domain decomposition algorithms that are well suited for solving linear systems on parallel computers.
Download or read book A Multigrid Tutorial written by William L. Briggs and published by SIAM. This book was released on 2000-07-01 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- Numerical Analysis.
Download or read book SIAM Journal on Scientific Computing written by and published by . This book was released on 2008 with total page 1402 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Analysis of an Aggregation based Algebraic Multigrid Method and Its Parallelization written by Meng-Huo Chen and published by . This book was released on 2014 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt: The interests of this thesis are twofold. First, a two-grid convergence analysis based on the paper [Algebraic analysis of aggregation-based multigrid by A. Napov and Y. Notay, Numer. Lin. Alg. Appl. 18 (2011), pp. 539-564 ] is derived for various aggregation schemes applied to a finite element discretization of a rotated anisotropic diffusion equation. As expected, it is shown that the best aggregation scheme is one in which aggregates are aligned with the anisotropy. In practice, however, this is not what automatic aggregation procedures do. We suggest an approach for determining appropriate aggregates based on eigenvectors associated with small eigenvalues of a block splitting matrix. In the second part of the thesis several issues regarding the parallel implementation of aggregation-based multigrid methods are discussed. The coarsest grid solving stage of multigrid cycles has been a bottleneck for parallel multigrid algorithms to attain a good speedup. A comparison between a parallel linear system direct solver (MUMPS) and a few steps of preconditioned conjugate gradient (PCG) methods for solving the coarsest grid system is carried out and tested on TACC Lonestar multi-processor machine. Regarding the preconditioner of conjugate gradient iterations, a parallel sparse approximate inverse (SAI) algorithm is used to construct an approximate inverse of the original matrix in order to replace the preconditioner solving step, which is inherently sequential, by matrix-vector multiplications. The linear systems tested arise from discretization of 2D or 3D partial differential equations, which are symmetric positive definite. The results exhibit that using PCG on the coarsest grid attains better speedup and overall better performance than MUMPS when the number of processors is greater than about 100. The effects of different decompositions of the physical domain (rows/slab versus blocks/pencils) on the scaling and efficiency of aggregation-based algebraic multigrid are also studied and one sees that the blocks/pencils decomposition of the physical domain reduces the amount of communication and hence has better performance.
Download or read book Multigrid Methods VI written by Erik Dick and published by Springer Science & Business Media. This book was released on 2000-08-28 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains 39 of the papers presented at the Sixth European Multigrid Conference, held in Gent, Belgium, September 27-30, 1999. The topics treated at the conference cover all aspects of Multigrid Methods: theory, analysis, computer implementation, applications in the fields of physics, chemistry, fluid mechanics, structural mechanics and magnetism.
Download or read book SIAM Journal on Computing written by Society for Industrial and Applied Mathematics and published by . This book was released on 1996 with total page 712 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Multi Grid Methods and Applications written by Wolfgang Hackbusch and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multi-grid methods are the most efficient tools for solving elliptic boundary value problems. The reader finds here an elementary introduction to multi-grid algorithms as well as a comprehensive convergence analysis. One section describes special applications (convection-diffusion equations, singular perturbation problems, eigenvalue problems, etc.). The book also contains a complete presentation of the multi-grid method of the second kind, which has important applications to integral equations (e.g. the "panel method") and to numerous other problems. Readers with a practical interest in multi-grid methods will benefit from this book as well as readers with a more theoretical interest.
Download or read book Multigrid Methods written by James H Bramble and published by Routledge. This book was released on 2019-01-22 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multigrid methods are among the most efficient iterative methods for the solution of linear systems which arise in many large scale scientific calculations. Every researcher working with the numerical solution of partial differential equations should at least be familiar with this powerful technique. This invaluable book presents results concerning the rates of convergence of multigrid iterations.
Download or read book Multigrid Methods IV written by P.W. Hemker and published by Birkhäuser. This book was released on 2012-12-06 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a selection from the papers presented at the Fourth European Multigrid Conference, held in Amsterdam, July 6-9,1993. There were 78 registered participants from 14 different countries, and 56 presentations were given. The preceding conferences in this series were held in Cologne (1981, 1985) and in Bonn (1990). Also at the other side of the Atlantic special multigrid conferences are held regularly, at intervals of two years, always in Copper Mountain, Colorado, US. The Sixth Copper Mountain Conference on Multigrid Methods took place in April, 1993. Circumstances prevented us from putting a larger time interval between the Copper and Amsterdam meetings. The next European meeting is planned in 1996, a year later than the next Copper Meeting. When the first multigrid conference was held in 1981 there was no doubt about the usefulness of a conference dedicated specially to multigrid, because multigrid was a new and relatively unexplored subject, still in a pioneering stage, and pursued by specialists. The past twenty years have shown a rapid growth in theoretical understanding, useful applications and widespread acceptance of multi grid in the applied disciplines. Hence, one might ask whether there is still a need today for conferences specially dedicated to multigrid. The general consensus is that the answer is affirmative. New issues have arisen that are best addressed or need also be addressed from a special multigrid point of view.
Download or read book Proceedings of the Fourth Copper Mountain Conference on Multigrid Methods written by Jan Mandel and published by SIAM. This book was released on 1989-01-01 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt:
